Unit Weight Of Water Given Effective Normal Stress Calculator

Formula Used:

\[ \gamma_{water} = \gamma_{saturated} - \frac{\sigma'}{z \times \left(\cos\left(\frac{i \times \pi}{180}\right)\right)^2} \]

Saturated Unit Weight of Soil (γ_saturated):

N/m³

Effective Normal Stress (σ'):

Depth of Prism (z):

Angle of Inclination (i):

degrees

Unit Weight of Water (γ_water):

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1. What is Unit Weight of Water?

Unit Weight of Water represents the weight per unit volume of water, typically measured in N/m³ or kN/m³. In soil mechanics, it's crucial for understanding buoyancy effects and effective stress calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{water} = \gamma_{saturated} - \frac{\sigma'}{z \times \left(\cos\left(\frac{i \times \pi}{180}\right)\right)^2} \]

Where:

\( \gamma_{water} \) — Unit weight of water (N/m³)
\( \gamma_{saturated} \) — Saturated unit weight of soil (N/m³)
\( \sigma' \) — Effective normal stress (Pa)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (degrees)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the unit weight of water based on saturated soil properties and effective stress conditions, accounting for inclined surfaces.

3. Importance of Unit Weight Calculation

Details: Accurate calculation of unit weight of water is essential for geotechnical engineering applications, including slope stability analysis, foundation design, and seepage calculations in soil mechanics.

4. Using the Calculator

Tips: Enter all values in appropriate units. Saturated unit weight and effective stress should be positive values. Depth must be greater than zero. Angle of inclination should be between 0-90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value for unit weight of water?
A: The unit weight of water is approximately 9810 N/m³ (9.81 kN/m³) at standard conditions.

Q2: Why is the angle of inclination important?
A: The angle affects the normal component of stress on inclined planes, which is crucial for accurate stress calculations in sloped terrain.

Q3: How does saturated unit weight differ from bulk unit weight?
A: Saturated unit weight includes the weight of both soil particles and water in completely saturated conditions, while bulk unit weight may include partially saturated conditions.

Q4: What is effective normal stress?
A: Effective normal stress is the stress carried by the soil skeleton, calculated as total stress minus pore water pressure.

Q5: When would this calculation be used in practice?
A: This calculation is commonly used in slope stability analysis, retaining wall design, and other geotechnical applications where water effects on soil strength need to be considered.